Looks like a complete non starter I'm afraid.
The specification states that the EcoloBlue 28 Atmospheric Water Generator will produce 5-7 gallons of water in the first 24 hrs. How much power does this thing use? According to the operational manual 480W continously. Or a total of about 12 KWhrs per day.
Here are the specifications for Honda EU20i i.e. 2000 W generator set.
http://hondagenerator.co.uk/pages/HondaEU20i.htmAt 1/4 load i.e 500W the Generator will run for 10 hrs and use 4.1 litres of fuel or just greater than about 1 US gallon.
So to produce 5-7 gallons of water you will need to burn over 2.5 gallons of petroleum. It would be cheaper and safer just to store the water for an emergency situation.
And the manufacturers have the nerve to put the prefix eco in the products name.